Queen's Park Rangers defender Anton Ferdinand refused to shake the hand of Chelsea's John Terry before a Premier League match on Saturday following allegations of racist comments by Terry to Ferdinand in a game last season.
"We have to move on. These things will separate us and become like some mafia feud," Taylor told BBC Radio Five.
The practice of opposing teams shaking hands before matches was introduced in the 2008-09 season as part of a "Get on with the game" initiative.
But despite the Ferdinand and Terry incident and similar controversial cases including one involving Liverpool's Luis Suarez and Manchester United's Patrice Evra, Taylor feels the goodwill gesture should remain part of the game.
"Owners, managers, chief executives and players said 'yes' (to the idea) and I do not know why we should say 'no' now," Taylor said.
"I would like to say to the players that I see no reason why they cannot do it (shake hands)," Taylor said.
"They are not betraying any personal principles. It is being done for the image of the game and to set the right example to the mascots and youngsters playing at school."
Terry was accused of racially abusing Ferdinand during a match last October but was cleared in court, though he still faces a Football Association charge over the incident.